DNA-lipid complexes: stability of honeycomb-like and spaghetti-like structures

A molecular level theory is presented for the thermodynamic stability of two (similar) types of structural complexes formed by (either single strand or supercoiled) DNA and cationic liposomes, both involving a monolayer-coated DNA as the central structural unit. In the "spaghetti" complex the central unit is surrounded by another, oppositely curved, monolayer, thus forming a bilayer mantle. The "honeycomb" complex is a bundle of hexagonally packed DNA-monolayer units. The formation free energy of these complexes, starting from a planar cationic/neutral lipid bilayer and bare DNA, is expressed as a sum of electrostatic, bending, mixing, and (for the honeycomb) chain frustration contributions. The electrostatic free energy is calculated using the Poisson-Boltzmann equation. The bending energy of the mixed lipid layers is treated in the quadratic curvature approximation with composition-dependent bending rigidity and spontaneous curvature. Ideal lipid mixing is assumed within each lipid monolayer. We found that the most stable monolayer-coated DNA units are formed when the charged/neutral lipid composition corresponds (nearly) to charge neutralization; the optimal monolayer radius corresponds to close DNA-monolayer contact. These conclusions are also valid for the honeycomb complex, as the chain frustration energy is found to be negligible. Typically, the stabilization energies for these structures are on the order of 1 k(B)T/A of DNA length, reflecting mainly the balance between the electrostatic and bending energies. The spaghetti complexes are less stable due to the additional bending energy of the external monolayer. A thermodynamic analysis is presented for calculating the equilibrium lipid compositions when the complexes coexist with excess bilayer.